The most important chains to research are these:
Planet Structures (up to +5's)
Hull (up to Nexus grids)
Energy (Up to Zero-point Energy)
Guns (Up to Antiprotons)
Scanners (up to Sub-Dimensional Sensors)
Research one tier of one, then move down the list, and keep cycling through until your have all of them doe. Then, you can start researching other things like cloak and defense.
Keep upping your research, until it gets to around 1500. Then, all into artifact. It is the most important stat in the game. (See more
here, or come join us at
The Invisible Storm).